I sympahtise because I have two children from my wife's first marriage, and we have a third daughter together.
The first and essential rule in dealing with step-children is a united front from you and your partner. Without that, you are lost. It's not just step-children - all children try and play one parent off against the other, that's normal, it just has additional ressonance when you are ths step-parent.
Your partner must back you at all times infront of the children - even if he thinks you are wrong, he must back you, and discuss it later when they are out of earshot. Once the rules are esablished and applied by both of you, you can start to get some sense of a family going.
Children respond to rules and discipline, it makes them feel secure, so you need to get the rules in place quickly, starting with a respectful way for everyone to talk to each other.
It will take a lot of patience, with firmness, but you will get there - IF you have ytour partner's support.
You must make sure he knows that if he can;t support you as a parental figure, then the relationship between all of you is not going to work, so you need to discuss this with him first. If he is unwilling to commit to supporting you in this, then you need to think very seriously about the future of ytour relationship.